NCERT Class 10 Mathematics

15

The theory of probabilities and the theory of errors now constitute

a formidable body of great mathematical interest and of great

practical importance.

• R.S. Woodward

15.1 Introduction

In Class IX, you have studied about experimental (or empirical) probabilities of events
which were based on the results of actual experiments. We discussed an experiment
of tossing a coin 1000 times in which the frequencies of the outcomes were as follows:

Head : 455 Tail : 545

Based on this experiment, the empirical probability of a head is

455

1000

, i.e., 0.455 and

that of getting a tail is 0.545. (Also see Example 1, Chapter 15 of Class IX Mathematics
Textbook.) Note that these probabilities are based on the results of an actual experiment
of tossing a coin 1000 times. For this reason, they are called experimental or empirical
probabilities. In fact, experimental probabilities are based on the results of actual
experiments and adequate recordings of the happening of the events. Moreover,
these probabilities are only ‘estimates’. If we perform the same experiment for another
1000 times, we may get different data giving different probability estimates.

In Class IX, you tossed a coin many times and noted the number of times it turned up
heads (or tails) (refer to Activities 1 and 2 of Chapter 15). You also noted that as the
number of tosses of the coin increased, the experimental probability of getting a head

(or tail) came closer and closer to the number

1

2

 Not only you, but many other

PROBABILITY